I disagree with this. It's hardly random.
Over the course of a long enough career (5 or more years), making it to the sweet sixteen is a good measure of a coach's ability to earn a favorable seed -- 5 or better (thus avoiding 1, 2 or 3 seeds in the 2d round) -- in the NCAA tourney. Coaches who can consistently do this (field a regular season top 20 or so team), will more likely than not, eventually make it to the second weekend. Coaches who can't will need a lot more luck than the coaches who can.
It's also a good measure of a coach's game prep ability, as well as his ability to adapt and overcome adversities such as venue, officiating, injury, etc. etc. in real time.
The NCAA Tourney is 3 two game tournaments. If a coach can't win at least the first one of those in a 20+ year career, I think it's fair to say that that coach has significant limitations, in one or more areas.
In a career of ten years or more, a sweet sixteen is a necessary but not (by itself) sufficient accomplishment for a coach to be considered "good" at the high major level.